Quadratic inequalities | Polynomial and rational functions | Algebra II | Khan Academy

Solving quadratic inequalities using factoring
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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[@khanacademy]

any number less than 3 is also less than 4 (so it can't be greater than 4)

[@chhabisarkar9057]

2020 and im still watching your videos!! can't appreciate the fact that your videos help me so much !! you are far better than my teacher !! thank you soooo much

[@jaga991]

u just explained what my teacher could'nt for 3 lessons, I really appreciate your videos keep it up!

[@drsumanadas]

Truest statement ever heard❤

[@rajsharma-uz3zd]

Excellent sir

[@mlgmelon]

Hows life treating you 8 years later

[@willking152]

how's life 8 months later@@mlgmelon

[@mlgmelon]

@@willking152 ups and downs but I'm good

[@extramailman12]

The way my teacher taught it to the class would involve about a page of work to solve a single quadratic inequality, this is literally like 1/5 of the work. Thanks

[@sharmainemararac8733]

Oh my gosh. Did i just understand what you said. Thank you so much.

[@JessCollinsss]

sharmaine mararac ikr this feels so good i have been so incapable of everything in maths for like a year

[@lifetimephysics8308]

@@JessCollinsss hi

[@agastyakarthik3098]

Did you just randomly say hi and expect a reply after years? ​@@lifetimephysics8308

[@kervincapangpangan7264]

youtube can be a substitute school in many means :D

[@wh4theduckquaaquaa]

after 8 years of posting the comment, I can say it really is a great substitute

[@aaryamangupta]

Kervin how r ya doing after 10 years m8

[@AhmedAli-fw8mb]

9 years ago wow

[@johnnyd1678]

Ahmed Ali ikr, and that was 2 years ago 🤓

[@camdamcool6125]

Wow I just realized that this was uploaded on my 4th birthday :0

[@salem6963]

2 years wow

[@saudal-gaithi6709]

11 years 🤯

[@k.ryashwanthreddy3265]

Now ,13 years ago. Wow

[@8arry94]

You helped me grasp this in 10 minutes whereas my algebra teacher wasn't able to over several classes. Thank you.

[@Ahmad-mc2rw]

Thank you so much! i am doing a levels and i was so depressed you explained me in 5 mins, god bless you!

[@mahnoorfatima9951]

That's so me... They don't explain this at all...

[@evertoncarpes]

This is amazing, your video was the first one I found here explaining it really algebraically (symbolically, instead of just appealing to graphic explanation). Your explanation is great because it forces one to see beyond the symbols, into the meaning of the expression. Thanks!

[@juanbaeza8411]

That's why people hate math so much I now realize, you're right, it has to make sense beyond the numbers.

[@Brian626]

thanks, my math classes barely taught me any of this stuff... its great to learn it

[@aaryamangupta]

How r ya after 15 years Brian?

[@amanchowdhury3644]

Watching this in 2022, Khan Academy is really one of the Greatest Learning Plattforms,

[@yamannajjar9546]

I was 2 years old when this video got posted and I’m taking benefits from it now

[@ritusingh8578]

14 years ago. Wow. He taught better than my teacher does in 2021. And he was so right that school teachers don't teach this, considering it "easy" while all of us are completely confused 🤦‍♀️

[@junkyarddog723]

I am watching this video in 2018(October) 😄😄😄😄😄😄

[@manavjangra7803]

same

[@fazrulsheikh4906]

I too

[@lindsaydavis6804]

Haha! Yep me in December

[@PikRabbit]

March 2019 for me

[@bibekbhattarai2729]

April 5 from me for Math 2

[@BTK-eo4hs]

"Hopefully, I can confuse you EVEN MORE!" 😂 Overall, you have awesome videos and a real talent for teaching. Thank you so much!!

[@lawliet2263]

This video is 13 years old but still it helped me Today!!!! Thanks Sal sir, for helping me!!!!

[@rhechard]

Bro made this just in time for my Ag2 test thanks

[@LetsVlogInCanada]

I had been looking for an explanation for this for soooooo long! Finally know the logic behind this! THANK YOU SAL! YOU ARE AMAZING!

[@uglymug211]

Having all the terms on one side is called the Null Factor Law. According to my Maths 10 B teacher...

[@johnnylonergan929]

As a mature student I struggle with remembering math from 20yrs ago and you SIR explain it in the correct way, [learning to walk before running] I give you an old Irish saying in thanks ' As you slide down the banister of life may all the splinters face the right way'

[@mayurkalsekar524]

good explanation sir!!! it helped in my study a lot

[@AAAKU25]

Ive never left a comment ever but i had to for sal khan, man taught this in a way my dum self could understand it.

[@phenomenalphysics3548]

My teacher just made me mug up the factorising inequalities, he never actually told what they meant and that made me so mad. But thank you so much sal.

[@ElisandroDeLeon]

Thank you so much. This video really helped.

[@INDIAN-yf5zg]

OLD IS GOLD⚡⚡⚡

[@asifiqbal9008]

I was searching for this video for the last 2 days . Every other video I found was trying to solve using short cut method.but this lecture really really felt good

[@Abhijeet_Arjeet]

2022 i still watched it my my it was helpful

[@walkinghumandisaster]

THANK YOU SO MUCH!

[@brittanydixon3798]

I really like how you explain this, your doing an outstanding job. as a kid I was very maladorit that had anything to do with math. this helps tremendously!!!!!

[@meredithpelt2405]

wow only if my teacher explained it like this

[@gog711]

PERFECT!!

[@mayaevans4444]

Helped a flipping ton

[@junkyarddog723]

Wooohh!! I was struggling to understand this for about half an year.. but understood in just 9:49 minutes in your video.. A big Thanks to you...

[@elyzh3r192]

KZbin just helped me go to highschool thx for teaching.

[@defiantprogram]

you don't know how much this...YOU have helped me through my educational life. I've had my fair share of bad teachers, but you're always here for students like us. Thank you so much for being the teacher i never had.

[@redjr242]

@BestCoolGuy22 simply replace x^2 with y into the equation then factor, solve and change the y back to x^2

[@20raeali12]

Thanks so much! This is more helpful than anything I learned in 5 years of math

[@stefanocosentinoo]

Thanks from Italy

[@devvrath123]

This is still helpful 13 years after. Thank you so much!!

[@xxRandomnameguyxx]

Jeez man, Ive been ripping my hair out trying to understand why my book jumped from an equation to its conclusion with out much explanation, then you come on here and BAM, actually Explain it. Thank you. I gets it.

[@sumeursault]

Sal's digital scratchpad has really come a long way since '07, lol. What a tremendous resource KA has become!

[@Arnob127]

helped a lot!!! thanks!

[@vaibhavverma6847]

Hi,Can you tell me that when i have to take Union of two solution sets?

[@FALLENx4NGEL]

Explained so much better than a major college dual enrollment program, you are a literal madlad.

[@Raiyun166]

So wait, we don't need to draw a stupid table everytime we do these questions? Wow. Thanks saves me time and gave me some intuition.

[@that_one_guy6243]

Thanks man really apprised it

[@Jorggee]

Thanks you taught something my teacher didn’t explain and wants us to do hw on

[@znhait]

This is in general very hard to teach. The main reason is that it's not all math. There are steps to follow but a bit of logic needs to be used and that is where most students get lost. First there is the logic of multiplying two numbers together whether they are positive or negative. The second is that using "and" and "or" with different two different inequalities. Last but not least, even writing the solution in interval form can be hard.

[@nghi1350]

Solving by discussing the signs of the 2 binomials consumes too much time. During tests/exams time is limited. The best and fastest way is to use the number line and the origin as test point.

[@oyj2542]

very helpful thank u

[@rupertstanely9172]

Love you man..! It's not confusing at all ...it was very simple ..! Great effort thanks...! Very simple step by step ...very easy to understand

[@ahsanbulbul8512]

Very easy to understand. Thank you so much for explaining this easy

[@xxRandomnameguyxx]

I really cant thank you enough.

[@aishashaikh9019]

Thank you so much for your help sir.

[@rokibulhasan2005]

You are just great...

[@mitchistiredandwobbly]

who would've thought while i was on my way on being born and this video was released, i had learn this within 14 years.

[@skusaid8512]

OMG!That was 12 years ago...

[@User-mb9qs]

the teachers at my public school are some of the worst teachers I have ever heard of. our school is also short staffed and has teachers teaching things that they shouldn't even be let near. these videos are basically my teacher now for math. if it weren't for you I honestly wouldn't have been able to pass algebra 2. thank you

[@file4318]

this is exactly what i was looking for, without using a visual graph

[@shauryaverma7232]

Salman sir u are great

[@ryo0812ca]

it's so funny how I understand the concept in under 10 minutes from this video, but when my teacher tried to explain it in an hour, he just ended up confusing me =S. THANK YOU!!!!

[@Yash_TwoBrothersOrganicFarms]

@1995a1995z 7:21 .I wouldnt like to delve into what Sal says from 7:37, but the bottomline you need to understand is that when (x-3)(x-4)

[@aucool7869]

my math teacher kept going on about zones and other dumb stuff like that thank you Sal for making my life easier

[@sharminakterruna6039]

This was so great

[@its_amlansarker]

Still helpful. 💙

[@bhawanisingh6006]

ty

[@lukzy3781]

14 years later and still the most valuable channel to highschool students

[@thatminecrafter3725]

This video is older than me😮

[@uddhavn]

12 years ago . O my god

[@tahaiftikhar298]

THANK YOU SO MUCHJ

[@sjrn85]

2020 and am still watching him love ❤️ what your doing keep it up!!!

[@senseiff8361]

It was 13 years ago!!!!!! Woahhh

[@SuzeRetardation]

thankyou so much

[@jes3233]

Thank you so much from my ♥

[@rtha490]

just wondering if maybe you could do a tutorial or tell me how you would the method backwards?

[@ankushpatidar2503]

Sir, you uploaded the video when I was 4 but I m watching when I am 17. Very nicely explained btw. THANK U SIR JI

[@sayshellooo]

Same, except i was 2 back then

[@idster7]

@darkhawk362 you're trying to divide 3.7 by 26.00? just move the decimal point over once to the right for each term: 37 divided by 260.

[@haseebahmad5853]

Excellent

[@iMintzGummie]

You are a BEAST

[@shubham3806]

your teaching is so goood....

[@kalyanisharma9208]

Perfect explaination ....👍

[@-IT-SugyanSuman]

Wonderful explanation I like you amazing explanation

[@brandiceMofucka]

Once again! i've learned and acheived good marks because of your tutoring :)

[@oaayush]

thank you very much......it was really very helpful.

[@ChinitaPhuongVyDinh]

Is there a video on how to use the squiggly line method to solve a quadratic inequality? that would be extremely helpful!

[@GoldGirlsGun]

Hi! I need help with this question please! I can't figure out how to factor this -6x^2 + 30x - 10 where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of at least $14,000 on the commodity? so -6x^2 + 30 - 10 ≥ 14,000

[@lunaromancia]

This just opened my third eye. Now I get why it's like that lol

[@tanxyrogue847]

Damn bro, now I don't always have 2 use the sign table. Tho I might ve failed a preCal test coz I didn't properly understand it (the sign table that is.) So children best you just learn em both lol.

[@UnitedPebbles]

Hey anyone ever take Q.A.? look at the magnitude of things and everything else is negligible! especially if the coefficients under square root is a negative number!

[@flarefiragax]

u sir, are a legend.

[@znhait]

I have a difficult time trying to teach students how to solve these problems. I haven't tried this method yet though. I usually use the number line method. This is similar to using the first derivative test, Inc/Dec, and CU/CD method in calculus. However, it's hard to explain to students why I have the roots of the quadratic as the points on the number line which could be explained by the IVT theorem from calculus but most students that are learning this are not in calculus.

[@loleklolkowski8567]

I just dodged a bullet thanks to the vid, youre a legend man!!

[@presstek2258]

ty this video helped so much

[@mamasboy6116]

this video is older than me!!

[@iamgroot2810]

Awesome explanation! Keep it up!

[@__-kn1vn]

What do you do if the equation isn't factorable?

[@sno-opy]

use trial and error

[@hinaahmad6770]

Quadratic formula

[@nimito_burrito]

use the quadratic formula?

[@chhabisarkar9057]

use the quadratic formula

[@RALMAR9]

agreed

[@1995a1995z]

@Optiyay ow right I understand, so when its a "- and a -" it becomes positive. and when its a - and + it becomes negative. Yeah thanks man :-)

[@parimtm]

what an explanation... cool 5/5¡